How does fossilisation actually happen?

Rarely, and through several different processes — the important point being that fossilisation requires an unusual sequence of events, which is why the fossil record is a biased sample of past life rather than a catalogue of it.

The usual fate of a dead organism is complete destruction: scavenging, decay by bacteria and fungi, and physical breakdown. Fossilisation requires that process to be interrupted.

What is normally required:

Rapid burial, before scavengers and decay destroy the remains. Sediment from floods, volcanic ash, tar or landslides.

Low oxygen, which slows decomposition — which is why deep water and stagnant conditions preserve so well.

Hard parts. Bones, shells, teeth and wood survive far better than soft tissue.

Undisturbed time, for the surrounding sediment to lithify.

Eventual exposure, through uplift and erosion, and discovery before weathering destroys it.

The processes:

Permineralisation. Mineral-rich water penetrates pore spaces and precipitates minerals within them. The original material may remain, with mineral filling the gaps — common for bone and wood.

Replacement. Original material dissolves and is replaced by minerals, sometimes preserving structure in remarkable detail.

Moulds and casts. The organism dissolves leaving a cavity — a mould — which may later fill with sediment to form a cast.

Carbonisation. Volatile components are driven off, leaving a thin carbon film, which preserves fine detail of leaves and soft-bodied organisms.

Preservation in amber, tar, ice or peat, which can retain soft tissue.

Trace fossils — footprints, burrows, coprolites — which record behaviour rather than anatomy and are genuinely informative about how animals moved and lived.

Why the record is biased, which matters for interpreting it:

Hard-bodied organisms are vastly over-represented.

Marine environments preserve far better than terrestrial ones.

Species with large populations and wide ranges appear more.

Some time periods and environments are barely represented, because the rocks were not preserved.

Lagerstätten are exceptional deposits preserving soft tissue and whole communities, and they are disproportionately important because they show what the ordinary record omits.